Using the position function , find the acceleration function.

Question

Using the position function  , find the acceleration function.

Quizplus · Accepted Answer

The acceleration function can be found by taking the second derivative of the position function. 
The position function is given by:
y(t) = 11e^(-0.2t)sin(5t)

Taking the derivative once gives the velocity function:
v(t) = y'(t) = -2.2e^(-0.2t)sin(5t) + 5e^(-0.2t)cos(5t)

Taking the derivative again gives the acceleration function:
a(t) = v'(t) = -4.4e^(-0.2t)cos(5t) - 5e^(-0.2t)sin(5t) - 1e^(-0.2t)sin(5t) - 25e^(-0.2t)cos(5t)

Simplifying this expression, we get:
a(t) = (11e^(-0.2t))(-4.4cos(5t) - 26sin(5t))

Therefore, the answer is C: 11eaa88b_9250_553e_a696_836b36260498_TB5869_11.

Using the Position Function , Find the Acceleration Function